Measuring the Kerr spin parameter of regular black holes from their shadow

TL;DR

This paper explores whether future high-resolution observations of black hole shadows can distinguish Kerr black holes from regular black holes like Bardeen and Hayward types, highlighting the challenges and potential constraints involved.

Contribution

It demonstrates the limitations of shadow measurements in differentiating Kerr from regular black holes, especially near extremal spins, and compares shadow-based spin estimates with other methods.

Findings

Shadow measurements can distinguish non-rotating black holes from Kerr.

For near-extremal black holes, all methods yield similar results, limiting deviation constraints.

Detecting a fast-rotating Kerr-like black hole can constrain the nature of the object.

Abstract

In a previous paper, one of us has showed that, at least in some cases, the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the "shadow" of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of the Kerr spin parameter of the Bardeen and Hayward regular black holes from their shadow, and we then compare the result with the estimate inferred from the K$\alpha$ iron line and from the frequency of the innermost stable circular orbit. For non-rotating black holes, the shadow approach provides different values, and therefore the Kerr black hole hypothesis can potentially be tested. For near extremal objects, all the approaches give quite similar results, and therefore it is not possible to constrain deviations from the Kerr solution. The present work confirms that it is definitively challenging to test this kind of metrics, even with future facilities. However, the detection of a source that looks like a fast-rotating Kerr black hole can put meaningful constraints on the nature of the compact object.